"Functional analysis is the branch of mathematics dealing with spaces of functions. It is a valuable tool in theoretical mathematics as well as engineering. It is at the very core of numerical simulation. In this class, the concepts of convergence and topology will be explained. You will understand the difference between strong convergence and weak convergence. You will also see how these two concepts can be used.

You will learn about different types of spaces including metric spaces, Banach Spaces, Hilbert Spaces and what property can be expected. You will see beautiful lemmas and theorems such as Riesz and Lax-Milgram and also Lp spaces, Sobolev spaces will be described. John Cagnol will provide a few details about PDEs, or Partial Differential Equations."

"The business world is at first sight a world of numbers. Accounting, algorithms, processes, quarterly figures, market shares, stock options, currency exchange rates etc. In all those areas, strong management tools exist and allow leaders to track their activities, improve their strategy, and overall run their company.

But another part the business world, equally important, has no numbers available. Corporate image, stress, creativity, team spirit, assertiveness, "black swans", aesthetics etc.

And a lack of rigor suddenly occurs with the excuse : "Since I can't measure, I can't manage... "

This is a mistake. The success of a business depends on its capacity to make a difference regarding competition. And today's differences in the eyes of a customer are probably built more on perception than on reality.

To help leaders to be rigorous even without figures, great philosophers have lots of ideas. Managers are invited to rediscover the art of thinking. They should understand the role of mental models, realize the importance of cognitive bias, agree on clear definitions and efficient criteria etc.

When one says, for example, "We should think creatively about the future of the company," our minds immediately focus on the word "company," which is part of the daily life. But it is important to split the sentence into 4 pieces and to pay some attention to three other key words namely "think", "creatively" and "future". They all must be considered as separated topics.

Creativity demands the ability to unshackle ourselves from conventional ways of thinking, to "think outside the box". But we need to go a step further. Once outside the box, we need to construct a new box or boxes (that is, new intellectual frameworks or models) to help us structure our thinking. Only once we have done so can we generate truly game-changing ideas."